Option 1: Jalaluddin Khilji - Jalaluddin Khilji was the founder of the Khilji dynasty and ruled the Delhi Sultanate from 1290 to 1296. However, his reign predates the establishment of the Vijayanagar Empire by Hari Har and Bukka.

Option 2: Alauddin Khilji - Alauddin Khilji was the second ruler of the Khilji dynasty and ruled the Delhi Sultanate from 1296 to 1316. Although his reign overlapped with the early years of the Vijayanagar Empire, he was not the Delhi Sultan during the establishment of the principality.

Option 3: Muhammad bin Tughlaq - Muhammad bin Tughlaq ruled the Delhi Sultanate from 1325 to 1351. He was known for his ambitious and often unsuccessful experiments, such as moving the capital from Delhi to Daulatabad. He was the Delhi Sultan when Hari Har and Bukka established the principality which later became the Vijayanagar Empire.

Option 4: Firoz Shah Tughlaq - Firoz Shah Tughlaq ruled the Delhi Sultanate from 1351 to 1388. While he was a